A theoretical model to analyze algebraic thinking and its application in school activities

This article illustrates research works characterized by the use of a common semiotic approach worked out by the authors on the learning of Algebra along the last two decades of SFIDA. We highlight the main phases of our work, namely: the use of Frege's semiotic triangle in order to investigate and describe the very nature of students' algebraic thinking in algebraic problem solving; the use of a semiotic analysis based on Frege's model in order to approach research questions on students' difficulties with inequalities; the passage from Frege's to Peirce's theoretical model in order to investigate new means of semiotic mediation based on digital technology to support students in Algebra learning; and finally, the phase centred on an extension of the notion of semiotic system in order to consider all semiotic resources acting in the thinking processes (towards the notion of "semiotic bundle"). This article also provides theoretical references used in other papers in this volume.